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When I read finance textbooks, I read things like "assume that the risk-free rate is equal to the yield on 30-year government bonds", "the government bond earns at the risk-free rate", "the cash is invested in a risk-free asset... such as government bonds", etc.

Are government bonds really risk-free? I find this hard to believe, especially for long-term government bonds (e.g. 30-year bonds). I also find it hard to believe that this applies to all government bonds of the world. In any given government's jurisdiction, isn't there some risk of natural disasters, societal collapse, revolution, conquest, etc.?

If government bonds are not risk-free, should the "risk-free rate" be lower than the yield on 30-year government bonds?

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    Put it this way, if the Government starts defaulting on bonds then the economy is going to have a real bad time, and ANY investment is going to be in big trouble.. In reality it is probably safer to say that it is the minimum risk you are going to get. – JohnFx Sep 13 '20 at 16:14
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United States Treasury bonds and notes are called "risk-free" because there is effectively zero risk of default by the lender. This is because the US Treasury can, if needed, simply "print money"* to pay its debts.

These bonds do carry other risks, for example that inflation could reduce the value of the payments below the original purchase amount.

And bonds from other governments, such as municipalities in the U.S., or even other national governments that don't control their own currency, do carry default risk. These governments also don't generally borrow at the same rate as the US Treasury does.

When I read finance textbooks, I read things like "assume that the risk-free rate is equal to the yield on 30-year government bonds", "the government bond earns at the risk-free rate", "the cash is invested in a risk-free asset... such as government bonds",

These were probably just written from a US-centric perspective. It doesn't apply to all governments, only to the one that the writer assumes most of their readers are familiar with.

I also find it hard to believe that this applies to all government bonds of the world.

It doesn't.

If government bonds are not risk-free, should the "risk-free rate" be lower than the yield on 30-year government bonds?

It depends how you're using the "risk-free rate". In many cases, you're just considering it as a kind of reference rate, or a base rate for comparing other investments.

In any given government's jurisdiction, isn't there some risk of natural disasters, societal collapse, revolution, conquest, etc.?

Any risk that could lead to default by the US Treasury would also very likely lead to default by other US issuers, so "risk-free" treasury bonds don't carry any risks that other bonds in the same market don't also carry.

Similarly, in other countries, if the economy collapses, or the country is conquered, other issuers selling bonds in that country's currency are likely to default (whether literally or effectively due to currency devaluation) along with the national government. So even though it isn't truly risk-free, the government's borrowing rate provides a useful reference for the rate paid by the lowest-risk borrowers in that market.

* The Treasury doesn't literally print paper money (that's a function of the federal reserve banks, which aren't technically part of the government), but could, in principle, produce a coin of arbitrary value.

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    Even more technically, FRB notes are printed (and designed) by BEP which is part of Treasury, but issued by FRB which receives the effective seigniorage. But FRB's profits, after certain reserves, are 'contributed' to Treasury General Fund, so the net result is basically the same as if FRB weren't there, except for the (nontrivial) logistics of storage and transport. :-? – dave_thompson_085 Sep 16 '20 at 5:42
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Sure, no investment is truly "risk free". Government bonds are generally very low risk, but the risk is not zero. Governments can and have repudiated debt, i.e. simply declared that they've decided they're not going to pay. The government could be overthrown in a revolution or conquered by an invading army. If you have a bond issued by the Confederate States of America or Tsarist Russia, sorry, it's not worth anything today. (Well, it may be valuable to a museum or a collector for its historical value.)

But a bond from a stable government is very low risk, about as close to zero risk as you're going to get. I would be very surprised, for example, if the US government were to default on government bonds. If they did, that would likely mean that the entire economy had collapsed or the government was in anarchy, at which point you probably have bigger things to worry about than a defaulted bond, and it's unlikely that any other investment you have is doing well either. Except for investments in a fortified bunker stocked with food, medicine, and weapons. So yeah, it's not zero, but it's very close to zero.

There are other countries where I would not make the same assessment. I wouldn't be quite so confident in a bond issued by the government of, say, Venezuela. Or less dramatically, Greece.

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    Greece is a brilliant example. Because as members of the Eurozone they do not control the priting of money. Hence any "monetarily sovereign" government can realistically never default. And US is sovereign over USD, Greece is not over EUR. – usr-local-ΕΨΗΕΛΩΝ Sep 15 '20 at 14:53
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    Even "monetarily sovereign" nations sometimes default. Argentina defaulted on its debt in 2001 and again just a few months ago -- though this last time they negotiated new payment terms to avoid total default. According to this article, cnn.com/2020/05/17/investing/stocks-week-ahead/index.html, Ecuador and Lebanon also defaulted on debt this year. And I think Pakistan defaulted recently. – Jay Sep 16 '20 at 2:22

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